# AS maths trig help

"In triangle DEF, ED = 5cm and EF = 6cm.
Given that sin(∠DEF) = and ∠DEF is acute.
(a) Find the exact value of cos(∠DEF)"

So I did arcsin(2/3) to get 41.8...degrees for the value of angle of DEF. However when I did cos (41.8...) I got 0.74.... I think this is wrong as the question asked for the exact answer but I'm only getting decimals. any tips?
BuMp
Is there a right angle in this triangle?
Original post by Gmart
Is there a right angle in this triangle?

So you have two sides of three, and no angles?
Original post by Gmart
So you have two sides of three, and no angles?

Yeah just given the length of two sides and the question implies that you have to solve for angle DEF to find the exact value of cos DEF
Original post by Soul Wavel3ngth
Yeah just given the length of two sides and the question implies that you have to solve for angle DEF to find the exact value of cos DEF

Original post by Gmart

Hehe yeah the question is a bit harsh lol. Should I just stick with my original answer?
Original post by Soul Wavel3ngth
Hehe yeah the question is a bit harsh lol. Should I just stick with my original answer?

If no answer is possible, you could choose any number, it will be equally wrong.

You could try making the EF distance different and then use the cosine rule to calculate a couple of answers to show that DEF varies.
Original post by Soul Wavel3ngth
"In triangle DEF, ED = 5cm and EF = 6cm.
Given that sin(∠DEF) = and ∠DEF is acute.
(a) Find the exact value of cos(∠DEF)"

So I did arcsin(2/3) to get 41.8...degrees for the value of angle of DEF. However when I did cos (41.8...) I got 0.74.... I think this is wrong as the question asked for the exact answer but I'm only getting decimals. any tips?

Just use the identity $\cos^2 \theta + \sin^2 \theta \equiv 1$ and the fact that this angle is acute in order to determine the exact cosine value of it.
(edited 3 years ago)
Original post by RDKGames
Just use the identity $\cos^2 \theta + \sin^2 \theta \equiv 1$ and the fact that this angle is acute in order to determine the exact cosine value of it.

Original post by Soul Wavel3ngth
"In triangle DEF, ED = 5cm and EF = 6cm.
Given that sin(∠DEF) = and ∠DEF is acute.
(a) Find the exact value of cos(∠DEF)"

So I did arcsin(2/3) to get 41.8...degrees for the value of angle of DEF. However when I did cos (41.8...) I got 0.74.... I think this is wrong as the question asked for the exact answer but I'm only getting decimals. any tips?

Maybe my computer didn't display that correctly - is sin theta 2/3?
Original post by Gmart
Maybe my computer didn't display that correctly - is sin theta 2/3?

Their post doesn't say it explicitly, but yes their working would imply this.
Original post by RDKGames
Their post doesn't say it explicitly, but yes their working would imply this.

ah must've been a mistake on my part. Yeah sin(DEF) = 2/3
Original post by Soul Wavel3ngth
ah must've been a mistake on my part. Yeah sin(DEF) = 2/3

Yep so just use the trig identity cos^x2+sinx^2=1. So substitute the value for sin(x) and you can work out cos(x) accordingly.
Original post by Icon4
Yep so just use the trig identity cos^x2+sinx^2=1. So substitute the value for sin(x) and you can work out cos(x) accordingly.

Ok thanks everyone